Modelling and Simulation of Complex Physical Systems

Dear Colleagues,

Classical Equilibrium Thermodynamics is considered to have begun its development with Carnot's famous "Reflections on the Motive Power of heat", first published in 1824. In this work, Carnot concluded that any cyclic process operating only between two different temperatures can always have an efficiency lower than that of an ideal engine, now called a Carnot engine.

This publication, and its later rediscovered results, paved the way for the formulation of the concept of entropy, proposed by Clausius in 1865, which made it possible to clearly formulate the concept of irreversibility through the Second Law of Thermodynamics.

However, by its very nature, Classical Equilibrium Thermodynamics does not address the effects of irreversibility on the efficiency of thermal cycles, as can be seen in the work of Fermi (1936). The most extensive discussion of this problem was made by Tolman and Fine (1948), who noted that a determination of the different irreversible processes that produce entropy within a heat engine makes it possible to evaluate the relative contributions of these processes to the inefficiency of the overall process in terms of lost useful work. But, the well-known Linear Irreversible Thermodynamics deals with the irreversibility of heat exchange processes but not with the efficiency of thermal cycles, and its founders did not pay much attention to this problem, as can be inferred from the writings of Onsager (1929), Meixner (1941, 1942, 1943), Prigogine (1947), and De Groot and Mazur (1962).

On the other hand, in nuclear power plants in 1957, independently of each other, Novikov and Chambadal noted that irreversible processes in the heat exchange between the reactor and its cooling system caused a decrease in plant efficiency. Later, in 1975, Curzon and Ahlborn analyzed the effect of the lack of thermal equilibrium between the reservoirs and the working substance during a Carnot-type cycle. Curzon and Ahlborn employed the formalism of Classical Equilibrium Thermodynamics, assuming that the working substance undergoes reversible internal transformations, while irreversibility occurs only in the couplings of the system with its surroundings. Although Alexandre Vaudrey, François Lanzetta, Michel Feidt (J. Non-Equilib. Thermodyn. 2014; 39 (4):199–203), and Michel Feidt (Entropy 2017, 19, 369; doi:10.3390/e19070369), have recently commented that the idea outlined by Curzon and Ahlborn had already been expounded by Jules Moutier in 1872, Henri B. Reitlinger in 1929 and Jacques Yvon in 1955; nevertheless it is necessary to recognize the formalization made by Curzon and Ahlborn. In addition, as A. Bejan (J. Appl. Phys., 79, 1996, pp 1191), and K.H. Hoffmann, J.M. Buzler, S. Schubert (J. Non-Equilib. Thermodyn. 22, 1997, pp. 311) have commented that finite-time thermodynamics is a method that combines, in a simple model, the basic concepts involved in heat transfer, fluid mechanics, and thermodynamics, with the aim of optimizing mechanisms and processes subject to finite size and time.

We are fifty years away from the publication of the seemingly simple work of Curzon and Ahlborn, and we have witnessed the variety of topics, problems, and applications that the concept of finite time has allowed us to develop: from the first reconstructions of the so-called Curzon–Ahlborn–Novikov–Chambadal efficiency to more recent applications such as an analytical approximation of optimal thermoeconomic efficiencies, or the application of the ecological criterion to analyze the well-known Feynmann mechanism, for example. In all of them, mathematics has undoubtedly played a central role in expressing, developing, and representing the results of the study of physical mechanisms and models with the idea of finite time, addressing topics such as so-called quantum machines, the modeling of energy-converting systems, and the development of algorithms that complement the basic principle of finite time in energy transfer processes.

Therefore, we cordially invite all those interested in so-called finite-time thermodynamics and related topics to contribute original results or review papes for a Special Issue addressing topics such as:

• Stability
• Modeling of thermal system
• Applied of the ecological criterion
• Finite time development
• Alternative objective function criterion
• some other similar issue

Prof. Dr. Delfino Ladino-Luna
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• stability
• finite time
• ecological function
• objective function
• thermodynamic optimization
• non-equilibrium thermodynamics
• algorithmic thermodynamics
• thermodynamic equations
• applied mathematical methods
• computational physics
• modeling of energy-converting systems
• modeling of energy systems
• modeling of thermal systems
• energy conversion modeling
• complex physical systems
• quantum thermodynamic machines
• quantum machine modeling